Edit Profile (opens in new tab) Cercignani, Carlo Co-Author Distance Author ID: cercignani.carlo Published as: Cercignani, Carlo; Cercignani, C. External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 205 Publications since 1962, including 15 Books 8 Contributions as Editor · 2 Further Contributions Biographic References: 7 Publications Co-Authors: 63 Co-Authors with 106 Joint Publications 1,619 Co-Co-Authors all top 5 Co-Authors 97 single-authored 14 Bobylev, Alexandre Vasiljévitch 14 Lampis, Maria 9 Illner, Reinhard 7 Kremer, Gilberto Medeiros 7 Lorenzani, Silvia 6 Martínez Gamba, Irene 5 Frezzotti, Aldo 4 Arkeryd, Leif O. 4 Majorana, Armando 4 Shinbrot, Marvin 3 Abbà, Antonella 3 Aoki, Kazuo 3 Cornille, Henri 3 Pagani, Carlo Domenico 3 Pulvirenti, Mario 3 Sgarra, Carlo 3 Valdettaro, Lorenzo 2 Bassanini, Piero 2 Biscari, Paolo 2 Fiszdon, Wladyslaw 2 Freotti, A. 2 Jerome, Joseph W. 2 Kogan, Mikhail Naumovich 2 Levermore, C. David 2 Penrose, Roger 2 Shu, Chi-Wang 2 Struckmeier, Jens 1 Akeryd, Leif 1 Albertoni, Sergio 1 Arnold, Anton 1 Arthur, M. D. 1 Batt, Jürgen 1 Battarra, Viliam 1 Bobrov, I. N. 1 Boffi, Vinicio C. 1 Bucci, Riccardo 1 Caflisch, Russel E. 1 Cannone, Marco 1 Cortese, Stefano 1 Desvillettes, Laurent 1 Ernst, Matthieu H. 1 Esposito, Raffaele 1 Gabetta, Ester 1 Gerasimenko, Viktor Ivanovich 1 Giurin, M. C. 1 Greenberg, William 1 Greppi, Mauro 1 Grosfils, Patrick 1 Guiraud, Jean-Pierre 1 Lampi, Maria 1 Lanford, Oscar E. III 1 Lebowitz, Joel Louis 1 Lentati, Andrea 1 Marra, Rossana 1 Mignemi, B. 1 Neudachin, Ilya 1 Nocilla, Silvio 1 Palczewski, Andrzej 1 Petrina, Dmitri Yakovych 1 Polewczak, Jacek 1 Protopopescu, Vladimir A. 1 Sattinger, David H. 1 Sharipov, Felix M. 1 Siewert, Charles E. 1 Slemrod, Marshall 1 Smolderen, Jean J. 1 Spohn, Herbert 1 Stoica, Cristina 1 Succi, Sauro 1 Takata, Shigeru 1 Tambi, R. 1 Tironi, Gino 1 Toscani, Giuseppe 1 Vigna, B. 1 Zweifel, Paul F. all top 5 Serials 31 Journal of Statistical Physics 23 Transport Theory and Statistical Physics 9 Physics of Fluids 7 Physics of Fluids 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Meccanica 6 Applied Mathematics Letters 4 Archive for Rational Mechanics and Analysis 4 Communications in Mathematical Physics 3 Computers & Mathematics with Applications 3 Journal of Mathematical Physics 3 Continuum Mechanics and Thermodynamics 2 Physics of Fluids, A 2 Mechanics Research Communications 2 European Journal of Mechanics. B. Fluids 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 Communications in Partial Differential Equations 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Applied Mathematical Sciences 2 Lecture Notes in Mathematics 2 Progress in Mathematical Physics 1 AIAA Journal 1 Archives of Mechanics 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 International Journal of Heat and Mass Transfer 1 Journal of Fluid Mechanics 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali 1 Duke Mathematical Journal 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rivista di Matematica della Università di Parma. Serie IV 1 Teoretichna i Prilozhna Mekhanika 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Surveys on Mathematics for Industry 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento 1 Annals of Physics 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Journal of Non-Equilibrium Thermodynamics 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Applied Mathematics 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Rivista di Matematica della Università di Parma. Serie 6 1 Comptes Rendus de l’Académie des Sciences. Série II. Fascicule b. Mécanique 1 Oberwolfach Reports 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Il Nuovo Cimento, X. Series 1 Istituto Lombardo, Accademia di Scienze e Lettere, Rendiconti, Sezione A 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 DMV Seminar 1 Mathematics and its Applications (Dordrecht) 1 Studies in Statistical Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Modeling and Simulation in Science, Engineering and Technology 1 Cambridge Texts in Applied Mathematics all top 5 Fields 163 Fluid mechanics (76-XX) 128 Statistical mechanics, structure of matter (82-XX) 25 Partial differential equations (35-XX) 19 Integral equations (45-XX) 9 Numerical analysis (65-XX) 8 General and overarching topics; collections (00-XX) 8 History and biography (01-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Mechanics of particles and systems (70-XX) 4 Quantum theory (81-XX) 3 Integral transforms, operational calculus (44-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of deformable solids (74-XX) 3 Relativity and gravitational theory (83-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Optics, electromagnetic theory (78-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 156 Publications have been cited 3,658 times in 2,459 Documents Cited by ▼ Year ▼ The Boltzmann equation and its applications. Zbl 0646.76001Cercignani, Carlo 839 1988 The mathematical theory of dilute gases. Zbl 0813.76001Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario 592 1994 Theory and application of the Boltzmann equation. Zbl 0403.76065Cercignani, Carlo 310 1975 Rarefied gas dynamics. From basic concepts to actual calculations. Zbl 0961.76002Cercignani, Carlo 162 2000 Mathematical methods in kinetic theory. Zbl 0191.25103Cercignani, C. 162 1969 Kinetic models for gas-surface interactions. Zbl 0288.76041Cercignani, C.; Lampis, M. 84 1971 The relativistic Boltzmann equation: Theory and applications. Zbl 1011.76001Cercignani, Carlo; Kremer, Gilberto Medeiros 79 2002 Mathematical methods in kinetic theory. 2nd ed. Zbl 0726.76083Cercignani, Carlo 78 1990 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324Bobylev, A. V.; Cercignani, C. 49 2003 Elementary solutions of the linearized gas-dynamics Boltzmann equation and their application to the slip-flow problem. Zbl 0114.22104Cercignani, C. 34 1962 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318Bobylev, A. V.; Cercignani, C.; Toscani, G. 31 2003 Slow rarefied flows. Theory and application to micro-electro-mechanical systems. Zbl 1097.82001Cercignani, Carlo 30 2006 Measure solutions of the steady Boltzmann equation in a slab. Zbl 0733.76063Arkeryd, Leif; Cercignani, Carlo; Illner, Reinhard 29 1991 Many-particle dynamics and kinetic equations. Zbl 0933.82001Cercignani, C.; Gerasimenko, V. I.; Petrina, D. Ya. 29 1997 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 27 2009 On the Boltzmann equation for rigid spheres. Zbl 0295.76048Cercignani, Carlo 26 1972 Moment equations for a granular material in a thermal bath. Zbl 1001.82092Bobylev, A. V.; Cercignani, C. 26 2002 Global existence of solutions for a model Boltzmann equation. Zbl 0960.82513Cercignani, C. 25 1987 Non-existence of a steady rarefied supersonic flow in a half-space. Zbl 0449.76056Arthur, M. D.; Cercignani, C. 25 1980 Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation. Zbl 0780.76066Arkeryd, Leif; Cercignani, Carlo 24 1990 High field approximations to a Boltzmann-Poisson system and boundary conditions in a semiconductor. Zbl 0894.76072Cercignani, C.; Gamba, I. M.; Levermore, C. D. 24 1997 Mathematical models in rarefied gas dynamics. Zbl 0850.76620Cercignani, C. 23 1991 A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal. Zbl 0789.76075Akeryd, Leif; Cercignani, Carlo 23 1993 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091Bobylev, A. V.; Cercignani, C. 22 2002 H-theorem and trend to equilibrium in the kinetic theory of gases. Zbl 0538.76068Cercignani, C. 21 1982 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 0917.01028Cercignani, Carlo 21 1998 Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Zbl 0966.76080Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 20 2000 On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation. Zbl 0688.76053Arkeryd, Leif; Cercignani, Carlo 20 1989 Monte Carlo simulation of the Taylor-Couette flow of a rarefied gas. Zbl 0785.76068Stefanov, Stefan; Cercignani, Carlo 19 1993 Flow of a rarefied gas past an axisymmetric body. II: Case of a sphere. Zbl 0172.54701Cercignani, C.; Pagani, C. D.; Bassanini, P. 18 1968 Shear flow of a granular material. Zbl 0990.82023Cercignani, C. 18 2001 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002Bobylev, A. V.; Cercignani, C. 17 2002 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090Bobylev, A. V.; Cercignani, C. 17 2002 Half-space problems in the kinetic theory of gases. Zbl 0594.76068Cercignani, C. 17 1986 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040Bobylev, Alexander V.; Cercignani, Carlo 16 1999 Analytic solution of the temperature jump problem for the BGK model. Zbl 0376.76055Cercignani, Carlo 16 1977 Existence of global solutions for the space inhomogeneous Enskog equation. Zbl 0629.76083Cercignani, Carlo 16 1987 A boundary value problem for discrete-velocity models. Zbl 0647.76050Cercignani, Carlo; Illner, Reinhard; Shinbrot, Marvin 16 1987 A drift-collision balance for a Boltzmann–Poisson system in bounded domains. Zbl 0987.82012Cercignani, C.; Gamba, I. M.; Levermore, C. D. 15 2001 Rayleigh-Bénard flow of a rarefied gas and its attractors. I: Convection regime. Zbl 1185.76355Stefanov, S.; Roussinov, V.; Cercignani, C. 14 2002 The Boltzmann equation and fluid dynamics. Zbl 1229.76093Cercignani, C. 14 2002 Plane Poiseuille flow with symmetric and nonsymmetric gas-wall interactions. Zbl 1076.82041Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 13 2005 Small data existence for the Enskog equation in \(L^ 1\). Zbl 1086.82540Cercignani, Carlo 13 1988 On the initial-boundary value problem for the Boltzmann equation. Zbl 0753.76151Cercignani, Carlo 12 1991 A remarkable estimate for the solutions of the Boltzmann equation. Zbl 0762.35090Cercignani, Carlo 12 1992 Discrete velocity models without nonphysical invariants. Zbl 0958.82041Bobylev, Alexander V.; Cercignani, Carlo 12 1999 Shock waves for a discrete velocity gas mixture. Zbl 0972.82072Cercignani, Carlo; Cornille, Henri 12 2000 The grad limit for a system of soft spheres. Zbl 0505.76088Cercignani, Carlo 12 1983 Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions. Zbl 0937.45007Cercignani, C.; Illner, R. 12 1996 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 12 2008 A boundary value problem for the two dimensional Broadwell model. Zbl 0668.76091Cercignani, Carlo; Illner, Reinhard; Shinbrot, Marvin 12 1988 On diffusive equilibria in generalized kinetic theory. Zbl 1051.82021Cercignani, Carlo; Illner, Reinhard; Stoica, Cristina 12 2001 Gaseous mixture slit flow at intermediate Knudsen numbers. Zbl 0767.76064Cercignani, Carlo; Sharipov, Felix 11 1992 Kinetic theories and the Boltzmann equation. Lectures given at the 1st 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), Held at Montecatini, Italy, June 10-18, 1981. Zbl 0536.00019 11 1984 Existence of homoenergetic affine flows for the Boltzmann equation. Zbl 0697.76089Cercignani, Carlo 11 1989 On the thermodynamics of a discrete velocity gas. Zbl 0811.76078Cercignani, Carlo 11 1994 On nonlinear stationary half-space problems in discrete kinetic theory. Zbl 1084.82561Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario; Shinbrot, Marvin 11 1988 Global weak solutions of the Boltzmann equation. Zbl 1097.82022Cercignani, Carlo 11 2005 The structure of an infinitely strong shock wave. Zbl 1149.76336Cercignani, Carlo; Frezzotti, Aldo; Grosfils, Patrick 10 1999 The Milne problem with a force term. Zbl 0899.76319Cercignani, C.; Marra, R.; Esposito, R. 10 1998 Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 1190.76022Cercignani, Carlo; Lorenzani, Silvia 10 2010 Nonequilibrium phenomena I: The Boltzmann equation. Zbl 0583.76004 10 1983 On the kinetic theory of a dense gas of rough spheres. Zbl 0677.76080Cercignani, Carlo; Lampis, Maria 10 1988 The Boltzmann equation and high altitude aerodynamics. Zbl 1112.76447Cercignani, Carlo 10 1997 Equilibrium states and trend to equilibrium in a gas according to the Boltzmann equation. Zbl 0723.76079Cercignani, C. 9 1990 Weak solutions of the Boltzmann equation and energy conservation. Zbl 0830.35107Cercignani, C. 9 1995 A new scattering kernel in kinetic theory of gases. Zbl 0874.76076Cercignani, Carlo; Lampis, Maria; Lentati, Andrea 9 1995 Scaling limits and models in physical processes. Zbl 0912.35149Cercignani, Carlo; Sattinger, David H. 9 1998 Discrete velocity models for mixtures. Zbl 0917.76075Bobylev, Alexander V.; Cercignani, Carlo 9 1998 Variational approach to gas flows in microchannels. Zbl 1187.76086Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 8 2004 Steady solutions of the nonlinear Boltzmann equation. Zbl 0914.76071Cercignani, Carlo 8 1998 Stokes paradox in kinetic theory. Zbl 0155.55503Cercignani, C. 8 1968 Flow of a rarefied gas past an axisymmetric body. I: General remarks. Zbl 0172.54602Cercignani, C.; Pagani, C. D. 8 1968 The Boltzmann equation approach to the shear flow of a granular material. Zbl 1001.76092Cercignani, Carlo 7 2002 Exact solutions of the Boltzmann equation. Zbl 0803.35151Cercignani, C. 7 1993 Analysis of subgrid scale models. Zbl 1100.76527Abbà, A.; Cercignani, C.; Valdettaro, L. 7 2003 Analysis of thermal, sound, and shear waves according to a relativistic kinetic model. Zbl 0603.76128Cercignani, Carlo; Majorana, Armando 7 1985 Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects. Zbl 1262.76087Cercignani, Carlo; Lampi, Maria; Lorenzani, Silvia 7 2006 Monte Carlo simulation of Bénard’s instability in a rarefied gas. Zbl 0764.76060Stefanov, S.; Cercignani, C. 6 1992 Are there more than five linearly-independent collision invariants for the Boltzmann equation? Zbl 0718.60113Cercignani, Carlo 6 1990 A sketch of the theory of the Boltzmann equation. Zbl 0465.76068Cercignani, Carlo 6 1978 Rayleigh-Bénard flow of a rarefied gas and its attractors. II: Cchaotic and periodic convective regimes. Zbl 1185.76356Stefanov, S.; Roussinov, V.; Cercignani, C. 6 2002 Bifurcation problems in fluid-mechanics. Zbl 0195.27401Cercignani, Carlo 6 1970 The paradox of the inverted temperature profiles between an evaporating and a condensing surface. Zbl 0586.76132Cercignani, C.; Fiszdon, W.; Freotti, A. 6 1985 A trace theorem in kinetic theory. Zbl 0744.45005Cannone, Marco; Cercignani, Carlo 5 1991 On a functional equation arising in the kinetic theory of gases. Zbl 0703.76062Arkeryd, Leif; Cercignani, Carlo 5 1990 On relativistic collisional invariants. Zbl 0964.82046Cercignani, C.; Kremer, G. M. 5 1999 Measure solutions for the steady linear Boltzmann equation in a slab. Zbl 0940.35165Cercignani, C.; Giurin, M. C. 5 1999 On partial indices for a matrix Riemann-Hilbert problem. Zbl 0483.76090Cercignani, C.; Siewert, C. E. 5 1982 Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas. Zbl 0834.76066Cercignani, Carlo; Cortese, Stefano 5 1994 New scattering kernel for gas-surface interaction. Zbl 0892.76076Cercignani, C.; Lampis, M. 5 1997 Bénard’s instability in kinetic theory. Zbl 0793.76042Cercignani, Carlo; Stefanov, Stefan 5 1992 Monte Carlo simulation of a channel flow of a rarefied gas. Zbl 0799.76065Stefanov, Stefan; Cercignani, Carlo 5 1994 Rarefied gas flow through long slots. Zbl 0422.76045Cercignani, Carlo; Neudachin, Ilya 5 1979 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 1095.01502Cercignani, Carlo 5 2006 Moment closure of the relativistic Anderson and Witting model equation. Zbl 0971.82516Cercignani, C.; Kremer, G. M. 5 2001 Influence of the accommodation coefficient on the heat transfer in a rarefied gas. Zbl 0182.28701Bassanini, P.; Cercignani, C.; Pagani, C. D. 5 1968 Temperature, entropy, and kinetic theory. Zbl 0945.82553Cercignani, Carlo 5 1997 Sur des critères d’existence globale en théorie cinétique discrète. (On some criteria of global existence in discrete kinetic theory). Zbl 0622.76080Cercignani, Carlo 5 1985 Kinetic theory with “bounce-back” boundary conditions. Zbl 0675.76081Cercignani, Carlo 5 1989 Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 1190.76022Cercignani, Carlo; Lorenzani, Silvia 10 2010 On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models. Zbl 1192.35126Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 27 2009 Generalized kinetic Maxwell type models of granular gases. Zbl 1298.76209Bobylev, A. V.; Cercignani, C.; Gamba, I. M. 12 2008 134 years of Boltzmann equation. Zbl 1156.82301Cercignani, Carlo 3 2008 BEM approaches and simplified kinetic models for the analysis of damping in deformable MEMS. Zbl 1195.76276Cercignani, C.; Frangi, A.; Lorenzani, S.; Vigna, B. 4 2007 Rayleigh-Bénard flow of a rarefied gas and its attractors. III: Three-dimensional computer simulations. Zbl 1182.76719Stefanov, S.; Roussinov, V.; Cercignani, C. 3 2007 On the Reynolds equation for linearized models of the Boltzmann operator. Zbl 1136.82018Cercignani, C.; Lampis, M.; Lorenzani, S. 2 2007 Transport phenomena and kinetic theory. Applications to gases, semiconductors, photons, and biological systems. Zbl 1109.82001 1 2007 Slow rarefied flows. Theory and application to micro-electro-mechanical systems. Zbl 1097.82001Cercignani, Carlo 30 2006 Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects. Zbl 1262.76087Cercignani, Carlo; Lampi, Maria; Lorenzani, Silvia 7 2006 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 1095.01502Cercignani, Carlo 5 2006 Weak solutions of the Boltzmann equation without angle cutoff. Zbl 1108.82037Cercignani, Carlo 2 2006 Estimating the solutions of the Boltzmann equation. Zbl 1110.82036Cercignani, Carlo 1 2006 Plane Poiseuille flow with symmetric and nonsymmetric gas-wall interactions. Zbl 1076.82041Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 13 2005 Global weak solutions of the Boltzmann equation. Zbl 1097.82022Cercignani, Carlo 11 2005 Variational approach to gas flows in microchannels. Zbl 1187.76086Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 8 2004 Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions. Zbl 1134.82324Bobylev, A. V.; Cercignani, C. 49 2003 Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials. Zbl 1119.82318Bobylev, A. V.; Cercignani, C.; Toscani, G. 31 2003 Analysis of subgrid scale models. Zbl 1100.76527Abbà, A.; Cercignani, C.; Valdettaro, L. 7 2003 Recent results in the kinetic theory of granular materials. Zbl 1255.76141Cercignani, Carlo 3 2003 Variational approach to plane Poiseuille flow with general boundary conditions. Zbl 1182.76945Cercignani, Carlo; Lampis, Maria; Lorenzani, Silvia 3 2003 The relativistic Boltzmann equation: Theory and applications. Zbl 1011.76001Cercignani, Carlo; Kremer, Gilberto Medeiros 79 2002 Moment equations for a granular material in a thermal bath. Zbl 1001.82092Bobylev, A. V.; Cercignani, C. 26 2002 Self-similar solutions of the Boltzmann equation and their applications. Zbl 1001.82091Bobylev, A. V.; Cercignani, C. 22 2002 The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation. Zbl 1025.44002Bobylev, A. V.; Cercignani, C. 17 2002 Exact eternal solutions of the Boltzmann equation. Zbl 1001.82090Bobylev, A. V.; Cercignani, C. 17 2002 Rayleigh-Bénard flow of a rarefied gas and its attractors. I: Convection regime. Zbl 1185.76355Stefanov, S.; Roussinov, V.; Cercignani, C. 14 2002 The Boltzmann equation and fluid dynamics. Zbl 1229.76093Cercignani, C. 14 2002 The Boltzmann equation approach to the shear flow of a granular material. Zbl 1001.76092Cercignani, Carlo 7 2002 Rayleigh-Bénard flow of a rarefied gas and its attractors. II: Cchaotic and periodic convective regimes. Zbl 1185.76356Stefanov, S.; Roussinov, V.; Cercignani, C. 6 2002 Self-similar solutions of the Boltzmann equation for non-Maxwell molecules. Zbl 1034.82046Bobylev, A. V.; Cercignani, C. 2 2002 Shear flow of a granular material. Zbl 0990.82023Cercignani, C. 18 2001 A drift-collision balance for a Boltzmann–Poisson system in bounded domains. Zbl 0987.82012Cercignani, C.; Gamba, I. M.; Levermore, C. D. 15 2001 On diffusive equilibria in generalized kinetic theory. Zbl 1051.82021Cercignani, Carlo; Illner, Reinhard; Stoica, Cristina 12 2001 Moment closure of the relativistic Anderson and Witting model equation. Zbl 0971.82516Cercignani, C.; Kremer, G. M. 5 2001 Large size planar discrete velocity models for gas mixtures. Zbl 0995.82512Cornille, Henri; Cercignani, Carlo 4 2001 Dispersion and absorption of plane harmonic waves in a relativistic gas. Zbl 1100.76560Cercignani, C.; Kremer, G. M. 1 2001 Rarefied gas dynamics. From basic concepts to actual calculations. Zbl 0961.76002Cercignani, Carlo 162 2000 Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Zbl 0966.76080Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 20 2000 Shock waves for a discrete velocity gas mixture. Zbl 0972.82072Cercignani, Carlo; Cornille, Henri 12 2000 A domain decomposition method for Silicon devices. Zbl 1028.82021Cercignani, Carlo; Gamba, Irene M.; Jerome, Joseph W.; Shu, Chi-Wang 5 2000 A class of planar discrete velocity models for gas mixtures. Zbl 0959.82023Cornille, Henri; Cercignani, Carlo 4 2000 Propagation phenomena in classical and relativistic rarefied gases. Zbl 1017.82043Cercignani, Carlo 4 2000 Trend to equilibrium of a degenerate relativistic gas. Zbl 0958.82042Cercignani, C.; Kremer, G. M. 3 2000 The velocity distribution function in an infinitely strong shock wave. Zbl 1184.76541Takata, Shigeru; Aoki, Kazuo; Cercignani, Carlo 2 2000 Time-derivatives and frame-invariance beyond Newtonian fluids. Zbl 1004.76073Biscari, Paolo; Cercignani, Carlo; Slemrod, Marshall 2 2000 Applications of a new model for the differential cross-section of a classical polyatomic gas. Zbl 0990.82024Cercignani, Carlo; Lampis, Maria; Struckmeier, Jens 1 2000 On the rate of entropy production for the Boltzmann equation. Zbl 0958.82040Bobylev, Alexander V.; Cercignani, Carlo 16 1999 Discrete velocity models without nonphysical invariants. Zbl 0958.82041Bobylev, Alexander V.; Cercignani, Carlo 12 1999 The structure of an infinitely strong shock wave. Zbl 1149.76336Cercignani, Carlo; Frezzotti, Aldo; Grosfils, Patrick 10 1999 On relativistic collisional invariants. Zbl 0964.82046Cercignani, C.; Kremer, G. M. 5 1999 Measure solutions for the steady linear Boltzmann equation in a slab. Zbl 0940.35165Cercignani, C.; Giurin, M. C. 5 1999 A new model for the boundary conditions of the Boltzmann equation. Zbl 0978.76080Cercignani, Carlo; Lampis, Maria 3 1999 Ludwig Boltzmann. The man who trusted atoms. Foreword by Sir Roger Penrose. Zbl 0917.01028Cercignani, Carlo 21 1998 The Milne problem with a force term. Zbl 0899.76319Cercignani, C.; Marra, R.; Esposito, R. 10 1998 Scaling limits and models in physical processes. Zbl 0912.35149Cercignani, Carlo; Sattinger, David H. 9 1998 Discrete velocity models for mixtures. Zbl 0917.76075Bobylev, Alexander V.; Cercignani, Carlo 9 1998 Steady solutions of the nonlinear Boltzmann equation. Zbl 0914.76071Cercignani, Carlo 8 1998 Measure solutions for the steady nonlinear Boltzmann equation in a slab. Zbl 0920.35156Cercignani, Carlo 3 1998 New models for the differential cross-section of a polyatomic gas in the frame of the scattering kernel theory. Zbl 0964.76079Cercignani, Carlo; Lampis, Maria; Struckmeier, J. 2 1998 Monte Carlo simulation of the propagation of a disturbance in the channel flow of a rarefied gas. Zbl 0911.76070Stefanov, S.; Cercignani, C. 2 1998 Anisotropy effects in LES simulation of turbulent flows. Zbl 0928.76052Abbà, A.; Cercignani, C.; Valdettaro, L. 1 1998 Many-particle dynamics and kinetic equations. Zbl 0933.82001Cercignani, C.; Gerasimenko, V. I.; Petrina, D. Ya. 29 1997 High field approximations to a Boltzmann-Poisson system and boundary conditions in a semiconductor. Zbl 0894.76072Cercignani, C.; Gamba, I. M.; Levermore, C. D. 24 1997 The Boltzmann equation and high altitude aerodynamics. Zbl 1112.76447Cercignani, Carlo 10 1997 New scattering kernel for gas-surface interaction. Zbl 0892.76076Cercignani, C.; Lampis, M. 5 1997 Temperature, entropy, and kinetic theory. Zbl 0945.82553Cercignani, Carlo 5 1997 Stress and heat flux in non-inertial reference frames. Zbl 0891.76077Biscari, Paolo; Cercignani, Carlo 4 1997 Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions. Zbl 0937.45007Cercignani, C.; Illner, R. 12 1996 Weak solutions of the Boltzmann equation and energy conservation. Zbl 0830.35107Cercignani, C. 9 1995 A new scattering kernel in kinetic theory of gases. Zbl 0874.76076Cercignani, Carlo; Lampis, Maria; Lentati, Andrea 9 1995 Errata: Weak solutions of the Boltzmann equation and energy conservation. Zbl 0841.35093Cercignani, C. 4 1995 Interaction of evaporating and condensing particles in the free-molecular regime. Zbl 1027.76643Kogan, M. N.; Bobrov, I. N.; Cercignani, C.; Frezzotti, A. 3 1995 On global existence theorems for the initial-boundary value problem for the Boltzmann equation. Zbl 0938.76095Cercignani, Carlo 1 1995 The mathematical theory of dilute gases. Zbl 0813.76001Cercignani, Carlo; Illner, Reinhard; Pulvirenti, Mario 592 1994 On the thermodynamics of a discrete velocity gas. Zbl 0811.76078Cercignani, Carlo 11 1994 Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas. Zbl 0834.76066Cercignani, Carlo; Cortese, Stefano 5 1994 Monte Carlo simulation of a channel flow of a rarefied gas. Zbl 0799.76065Stefanov, Stefan; Cercignani, Carlo 5 1994 An explicitly solvable kinetic model for semiconductors. Zbl 0839.76075Cercignani, Carlo 4 1994 Mathematical problems in the gas dynamics of high-altitude flight. Zbl 0852.76081Cercignani, C. 3 1994 A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal. Zbl 0789.76075Akeryd, Leif; Cercignani, Carlo 23 1993 Monte Carlo simulation of the Taylor-Couette flow of a rarefied gas. Zbl 0785.76068Stefanov, Stefan; Cercignani, Carlo 19 1993 Exact solutions of the Boltzmann equation. Zbl 0803.35151Cercignani, C. 7 1993 On the absence of motion in certain nonequilibrium states of gases and vapors in free-molecular regime: General considerations and pipe flow. Zbl 0795.76070Cercignani, Carlo; Frezzotti, Aldo; Kogan, Mikhail N. 1 1993 A remarkable estimate for the solutions of the Boltzmann equation. Zbl 0762.35090Cercignani, Carlo 12 1992 Gaseous mixture slit flow at intermediate Knudsen numbers. Zbl 0767.76064Cercignani, Carlo; Sharipov, Felix 11 1992 Monte Carlo simulation of Bénard’s instability in a rarefied gas. Zbl 0764.76060Stefanov, S.; Cercignani, C. 6 1992 Bénard’s instability in kinetic theory. Zbl 0793.76042Cercignani, Carlo; Stefanov, Stefan 5 1992 Half-range completeness for the Fokker-Planck equation with an external force. Zbl 0925.60060Cercignani, C.; Sgarra, C. 4 1992 Measure solutions of the steady Boltzmann equation in a slab. Zbl 0733.76063Arkeryd, Leif; Cercignani, Carlo; Illner, Reinhard 29 1991 Mathematical models in rarefied gas dynamics. Zbl 0850.76620Cercignani, C. 23 1991 On the initial-boundary value problem for the Boltzmann equation. Zbl 0753.76151Cercignani, Carlo 12 1991 A trace theorem in kinetic theory. Zbl 0744.45005Cannone, Marco; Cercignani, Carlo 5 1991 Mathematical methods in kinetic theory. 2nd ed. Zbl 0726.76083Cercignani, Carlo 78 1990 Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation. Zbl 0780.76066Arkeryd, Leif; Cercignani, Carlo 24 1990 Equilibrium states and trend to equilibrium in a gas according to the Boltzmann equation. Zbl 0723.76079Cercignani, C. 9 1990 Are there more than five linearly-independent collision invariants for the Boltzmann equation? Zbl 0718.60113Cercignani, Carlo 6 1990 On a functional equation arising in the kinetic theory of gases. Zbl 0703.76062Arkeryd, Leif; Cercignani, Carlo 5 1990 On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation. Zbl 0688.76053Arkeryd, Leif; Cercignani, Carlo 20 1989 Existence of homoenergetic affine flows for the Boltzmann equation. Zbl 0697.76089Cercignani, Carlo 11 1989 ...and 56 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,188 Authors 76 Cercignani, Carlo 45 Toscani, Giuseppe 35 Aoki, Kazuo 31 Dimarco, Giacomo 31 Spiga, Giampiero 31 Yang, Tong 29 Pareschi, Lorenzo 29 Yun, Seok-Bae 28 Takata, Shigeru 27 Bisi, Marzia 27 Siewert, Charles E. 26 Degond, Pierre 26 Martínez Gamba, Irene 26 Yushkanov, Aleksandr Alekseevich 25 Desvillettes, Laurent 24 Bobylev, Alexandre Vasiljévitch 24 Golse, François 23 Sharipov, Felix M. 22 Carrillo de la Plata, José Antonio 22 Pulvirenti, Mario 22 Sone, Yoshio 20 Duan, Renjun 20 Kremer, Gilberto Medeiros 20 Latyshev, Anatolii Vasil’evich 20 Mouhot, Clément 19 Groppi, Maria 19 Klar, Axel 19 Torrilhon, Manuel 18 Arkeryd, Leif O. 18 Guo, Yan 18 Hu, Jingwei 17 Frezzotti, Aldo 17 Illner, Reinhard 17 Liu, Shuangqian 17 Saint-Raymond, Laure 17 Wagner, Wolfgang 17 Zhang, Xianwen 15 Esposito, Raffaele 15 Struchtrup, Henning 14 Carlen, Eric Anders 14 Khachatryan, Khachatur Aghavardovich 14 Shu, Chi-Wang 14 Van der Mee, Cornelis Victor Maria 14 Zhao, Huijiang 13 Bellomo, Nicola 13 Briant, Marc 13 Gordevs’kyĭ, Vyacheslav Dmytrovych 13 Marra, Rossana 13 Mieussens, Luc 13 Simonella, Sergio 12 Greenberg, William 12 Hauck, Cory D. 12 Majorana, Armando 12 Reese, Jason M. 12 Strain, Robert M. 12 Zanella, Mattia 11 Gibelli, Livio 11 Ha, Seung-Yeal 11 Jin, Shi 11 Lebowitz, Joel Louis 11 Li, Zhihui 11 Loyalka, S. K. 11 Morimoto, Yoshinori 11 Nouri, Anne 11 Perthame, Benoît 11 Rey, Thomas 11 Valougeorgis, Dimitris 11 Wennberg, Bernt 11 Wu, Lei 11 Yu, Shih-Hsien 10 Alexandre, Radjesvarane 10 Emerson, David R. 10 Filbet, Francis 10 García-Perciante, Ana Laura 10 Garcia, Roberto D. M. 10 Kim, Chanwoo 10 Lachowicz, Mirosław 10 Lampis, Maria 10 Lods, Bertrand 10 Lorenzani, Silvia 10 Santos, Andrés 10 Ukai, Seiji 10 Yu, Hongjun 10 Zhang, Yonghao 9 Caflisch, Russel E. 9 Doi, Toshiyuki 9 Fournier, Nicolas 9 Fox, Rodney O. 9 Gallagher, Isabelle 9 Hadjiconstantinou, Nicolas G. 9 Khachatryan, Aghavard Khachaturovich 9 Martalò, Giorgio 9 Monaco, Roberto 9 Nota, Alessia 9 Ohwada, Taku 9 Polewczak, Jacek 9 Regazzini, Eugenio 9 Sader, John E. 9 Slemrod, Marshall 9 Taguchi, Satoshi ...and 2,088 more Authors all top 5 Cited in 291 Serials 227 Journal of Statistical Physics 177 Journal of Computational Physics 119 Transport Theory and Statistical Physics 103 Physics of Fluids 87 Archive for Rational Mechanics and Analysis 74 Kinetic and Related Models 62 Communications in Mathematical Physics 59 Journal of Fluid Mechanics 59 Journal of Differential Equations 58 European Journal of Mechanics. B. Fluids 44 ZAMP. Zeitschrift für angewandte Mathematik und Physik 42 Computers and Fluids 41 Journal of Mathematical Analysis and Applications 41 Physica A 41 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 40 Computers & Mathematics with Applications 40 Journal of Mathematical Physics 38 Fluid Dynamics 35 Theoretical and Mathematical Physics 31 SIAM Journal on Mathematical Analysis 31 Continuum Mechanics and Thermodynamics 24 Journal of Scientific Computing 22 Physica D 21 Mathematical Methods in the Applied Sciences 19 Applied Mathematics Letters 18 Meccanica 17 Communications on Pure and Applied Mathematics 17 Communications in Partial Differential Equations 16 Computational Mathematics and Mathematical Physics 15 Applied Mathematics and Computation 14 Multiscale Modeling & Simulation 13 Computer Methods in Applied Mechanics and Engineering 13 Journal of Computational and Applied Mathematics 13 Journal of Functional Analysis 13 SIAM Journal on Scientific Computing 11 Computer Physics Communications 11 Physics of Fluids 11 Physics of Fluids, A 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Mathematical and Computer Modelling 11 Annals of Physics 10 SIAM Journal on Numerical Analysis 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Physics Letters. A 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Quarterly of Applied Mathematics 9 The Annals of Applied Probability 9 International Journal of Computational Fluid Dynamics 9 Nonlinear Analysis. Real World Applications 9 Journal of Statistical Mechanics: Theory and Experiment 8 Mathematics of Computation 8 Acta Applicandae Mathematicae 8 Discrete and Continuous Dynamical Systems 8 Foundations of Physics 7 General Relativity and Gravitation 7 Physics Reports 7 Ukrainian Mathematical Journal 7 Inventiones Mathematicae 7 SIAM Journal on Applied Mathematics 7 Stochastic Processes and their Applications 7 Communications in Computational Physics 7 Nonlinear Analysis. Theory, Methods & Applications 7 Journal of Computational and Theoretical Transport 6 International Journal of Heat and Mass Transfer 6 Journal of Mathematical Biology 6 Advances in Mathematics 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Mathematics and Computers in Simulation 6 Probability Theory and Related Fields 6 Bulletin of the American Mathematical Society. New Series 6 Matematicheskoe Modelirovanie 6 Journal of Physics A: Mathematical and Theoretical 6 Science China. Mathematics 6 Annals of PDE 5 Acta Mechanica 5 International Journal of Engineering Science 5 International Journal for Numerical Methods in Fluids 5 Mathematical Notes 5 Rendiconti del Seminario Matemàtico e Fisico di Milano 5 Siberian Mathematical Journal 5 Applied Mathematical Modelling 5 Journal of Nonlinear Science 5 Abstract and Applied Analysis 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Séminaire Laurent Schwartz. EDP et Applications 5 SN Partial Differential Equations and Applications 4 Applicable Analysis 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Integral Equations and Operator Theory 4 Applied Numerical Mathematics 4 Acta Mathematicae Applicatae Sinica. English Series 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Living Reviews in Relativity 4 Journal of Evolution Equations 4 Communications on Pure and Applied Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 SIAM/ASA Journal on Uncertainty Quantification ...and 191 more Serials all top 5 Cited in 49 Fields 1,508 Fluid mechanics (76-XX) 1,293 Statistical mechanics, structure of matter (82-XX) 935 Partial differential equations (35-XX) 352 Numerical analysis (65-XX) 155 Integral equations (45-XX) 128 Probability theory and stochastic processes (60-XX) 124 Classical thermodynamics, heat transfer (80-XX) 80 Biology and other natural sciences (92-XX) 59 Operator theory (47-XX) 59 Relativity and gravitational theory (83-XX) 58 Quantum theory (81-XX) 44 Mechanics of deformable solids (74-XX) 40 Dynamical systems and ergodic theory (37-XX) 39 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 37 Ordinary differential equations (34-XX) 34 Optics, electromagnetic theory (78-XX) 21 Astronomy and astrophysics (85-XX) 21 Operations research, mathematical programming (90-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 19 Mechanics of particles and systems (70-XX) 18 Functional analysis (46-XX) 15 Statistics (62-XX) 14 Computer science (68-XX) 13 Integral transforms, operational calculus (44-XX) 13 Information and communication theory, circuits (94-XX) 11 Systems theory; control (93-XX) 10 Real functions (26-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Approximations and expansions (41-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Special functions (33-XX) 6 General and overarching topics; collections (00-XX) 6 Difference and functional equations (39-XX) 6 Differential geometry (53-XX) 5 History and biography (01-XX) 4 Measure and integration (28-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Geophysics (86-XX) 2 Functions of a complex variable (30-XX) 2 General topology (54-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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